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Chapter 13: Q 17. (page 1066)

What geometric conditions do you look for when you are deciding which coordinate system to use when you are evaluating a triple integral?

Short Answer

Expert verified

The geometric condition we look for while deciding which coordinate system to use when evaluating a triple integral is region of integration.

Step by step solution

01

Given Information

We need to choose the geometric conditions while deciding coordinate system while evaluating a triple integral.

02

Simplification

The region of integration determine the type of coordinate system for simplification of the problem.
The coordinate system that determine the region of integration in easiest and simplest manner of taken for solving triple integral.

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Most popular questions from this chapter

Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.

$\int_{- 1}^{5} \int_{- 3}^{2} \int_{4}^{8} f (x, y, z) d z d x d y$

$How many summands are in \sum_{j = 3}^{13} \sum_{k = 5}^{20} \frac{j^{2}}{e^{jk}} ?$

Describe the three-dimensional region expressed in each iterated integral:

$\int_{- 2}^{4} \int_{2}^{6} \int_{0}^{5} f (x, y, z) d y d x d z$

Discuss the similarities and differences between the definition of the definite integral found in Chapter 4 and the definition of the double integral found in this section.

In Exercises 61–64, let R be the rectangular solid defined by

$R = \{(x, y, z) | 0 \leq a_{1} \leq x \leq a_{2}, 0 \leq b_{1} \leq y \leq b_{2}, 0 \leq c_{2} \leq z \leq c_{2}\} .$

Assume that the density of R is uniform throughout.

(a) Without using calculus, explain why the center of

mass is $(\frac{a_{1} + a_{2}}{2}, \frac{b_{1} + b_{2}}{2}, \frac{c_{1} + c_{2}}{2}) .$

(b) Verify that $(\frac{a_{1} + a_{2}}{2}, \frac{b_{1} + b_{2}}{2}, \frac{c_{1} + c_{2}}{2})$ is the center of mass by using the appropriate integral expressions.

See all solutions

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